The present invention relates to a method of statistically characterizing structural features in polymers. It finds particular application in conjunction with predicting and/or characterizing the mechanical behavior of rubber, and will be described with particular reference thereto. It is to be appreciated, however, that the present invention is also applicable to predicting and/or characterizing the mechanical behavior of other hyperelastic solids.
Traditionally, polymer product or structure designs, such as, for example, for seals, gaskets, and tires, have been developed on the basis of prior experience, part prototyping, and extensive experimental testing. While this method ultimately leads to adequate product designs, it is extremely costly, both in time and money. Consequently, with the advent of such technologies, as, for example, nonlinear Finite Element Analysis (FEA) and the associated computing technology, the trial and error methods of experimental testing can be largely replaced.
Finite Element Analysis is a structural analysis tool in which any product or structure, such as a tire, is segmented into fine elements and analyzed using calculations by means of a computer nor other appropriate processor. FEA allows a polymer design engineer to look at the behavior of a particular product without the expensive manufacturing and testing that is typically required in many conventional polymer product design processes. Moreover, FEA eliminates the lengthy trial and error process in polymer product design and reduces tool costs. FEA is also capable of evaluating the effects of material changes on a given product configuration by understanding deformation and stress patterns within the product geometry.
However, the accuracy of FEA is largely dependent upon accurate characterization and/or modeling of the product's material properties and geometry. While the deformation-related properties of metals, which are most often subject to FEA, are typically modeled using linear stress-strain equations, polymers such as rubbers exhibit nonlinear stress-strain relations even for the relatively small deformations experienced during normal use. The nonlinearity of the stress-strain relations of these materials is their specific trait and extends over the entire range of deformation, which is extremely large if compared with that of metals. In other words, polymers are hyperelastic materials, which typically exhibit nonlinear constitutive behavior. This behavior is a consequence of their macro-molecular structure.
The statistical description of macro-molecular chain length in polymers, as typically applied to the study of polymer rheology, is isotropic Gaussian in nature. The Mooney-Rivlin linear model of hyperelasticity, for example, is known to relate to such a statistical description. The general validity of this statistical characterization, however, is not conclusively confirmed by experiments. Rather, experiments typically reveal a type of non-linear behavior for polymers, which is inconsistent with the idea of a Gaussian statistical description of the polymer chain length, which governs the rubber deformation. However, little is known beyond the Mooney-Rivlin connection between nonlinear constitutive behavior of polymers and their statistical description.
The present invention contemplates a new and improved method for determining fundamental properties of rubbers based on the idea that the macromolecular chain statistics is directly reflected in fundamental properties. Consequently, we determine the microstructure of hyperelastic materials directly from macro-level physical experiments.